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On black holes in BMN plane wave Hsien-Hang, Shieh

Abstract

In this thesis, we attempt to construct a black hole solution with BMN plane wave asymptotics. We find it to be a very complicated problem. Through explicit computations, we showed the Penrose limit of the Schwarzschild Anti de-Sitter spacetime do not result "in a background with event horizon, in accord with the no go theorems reviewed which suggest the symmetries of plane wave spacetimes are not compatible with the existence of regular event horizon. The detailed boundary and light cone structure of the BMN spacetime are studied. It is made clear that the conformal boundary of the plane wave is not related to the boundary of Anti-de Sitter. In order to understand the concept of temperature and thermal state in the BMN background, we study the response of an Unruh monople detector following various trajectories. The detector response function shows the vacuum state natural to the BMN plane wave has very different thermal behavior from the Minkowski vacuum. In particular, observers following any Killing trajectory will not regard the plane wave vacuum as a thermal state. This result can be viewed as a semi-classical verification of the no-go theorems. We also review the solution generating technique, the null Melvin twist and the correspondence principle of the black string solutions so generated in the plane wave geometry.

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